Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type Inequalities, and Applications to Riesz Potentials and p-sub-Laplacian Systems

Kassymov A. Ruzhansky M. Suragan D.
December 2023 Springer

Potential Analysis
2023 #59 Issue 4 1971 - 1994 pp.

In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyapunov-type inequality for the Riesz potential on homogeneous Lie groups. The obtained Lyapunov inequality for the Riesz potential is new already in the classical setting of ℝ^N. As an application, we give two-sided estimate for the first eigenvalue of the Riesz potential. Also, we obtain Lyapunov inequality for the system of the fractional p-sub-Laplacian equations and give an application to estimate its eigenvalues.

Fractional Caffarelli-Kohn-Nirenberg inequality , Fractional Gagliardo-Nirenberg inequality , Fractional Lyapunov-type inequality , Homogeneous Lie group

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Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
School of Mathematical Sciences, Queen Many University of London, London, United Kingdom
Department of Mathematics, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Ave, Astana, 010000, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
Department of Mathematics
School of Mathematical Sciences
Department of Mathematics

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